A proof of Ross's conjecture for two-site moving-target search

@misc{li2026proof,
  title = {{A proof of Ross's conjecture for two-site moving-target search}},
  author = {Yunpeng Li},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.09368},
  eprint = {2608.09368},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.09368},
}

TY  - UNPB
TI  - A proof of Ross's conjecture for two-site moving-target search
AU  - Yunpeng Li
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2608.09368
UR  - https://arxiv.org/abs/2608.09368
AB  - A target moves between two sites according to a discrete-time Markov chain with a 2×2 transition matrix M. At each epoch one site is searched at positive cost, and a search may overlook a target that is present. Ross conjectured that an optimal policy is threshold in the posterior probability that the target is at site~1. MacPhee and Jordan proved the conjecture throughout the nonpositive-determinant (det M≤0) regime and for part of the positive-determinant (det M>0) regime, leaving the remaining cases open. We prove threshold optimality throughout the positive-determinant regime, completing Ross's conjecture for all parameter values.
ER  -